In optical communication systems that employ coherent optical receivers, the modulated optical signal received at the coherent receiver is mixed with a narrow-line-width local oscillator (LO) signal, and the combined signal is made incident on one or more photodetectors. The frequency spectrum of the electrical current appearing at the photodetector output(s) is substantially proportional to the convolution of the received optical signal and the local oscillator (LO), and contains a signal component lying at an intermediate frequency that contains data modulated onto the received signal. Consequently, this “data component” can be isolated and detected by electronically filtering and processing the photodetector output current.
The LO signal is typically produced using a semiconductor laser, which is typically designed to have a frequency that closely matches the frequency of the laser producing the carrier signal at the transmitter. However, as is known in the art, such semiconductor lasers exhibit a finite line width from non-zero phase noise. As a result, frequency transients as high as ±400 MHz at rates of up to 50 kHz are common. This frequency offset creates an unbounded linear ramp in the phase difference between the two lasers. In addition, many such lasers often exhibit a line width of the order of 1 MHz with a Lorentzian spectral shape. As a result, even if the transmitter and LO lasers were to operate at exactly the same average frequency, a phase error linewidth of about ±2 MHz can still exist. This Lorentzian spectrum creates a phase variance that grows linearly with time, and the initial phase difference is random, so over the lifetime of operation of the optical connection the phase error is unbounded.
As is known in the art, data is typically encoded in accordance with a selected encoding scheme (eg Binary Phase shift Keying (BPSK); Quadrature Phase Shift Keying (QPSK), 16-Quadrature Amplitude Modulation (16-QAM) etc.) to produce symbols having predetermined amplitude and phase. These symbols are then modulated onto an optical carrier for transmission through the optical communications system to a receiver. At the receiver, the received optical signal is processed to determine the most likely value of each transmitted symbol, so as to recover the original data.
As is known in the art, a frequency mismatch or offset Δf, and independent phase noise, between the transmitter and LO laser appears as a time-varying phase error between detected symbols and the correct (or ideal) phase of the corresponding transmitted symbols as determined by the applicable encoding scheme. This phase error is exacerbated by phase non-linearities of the optical communications system, and in particular, cross-phase modulation (XPM). This phase error is unbounded, in that it tends to follow a ramp plus a Brownian random-walk trajectory and can rise to effectively infinite multiples of 2π.
As is known in the art, because the phase error is unbounded, it cannot be compensated by a bounded filtering function. However, an unbounded filtering function is susceptible to cycle slips, as will be described in greater detail below.
Applicant's U.S. Pat. No. 7,606,498 entitled Carrier Recovery in a Coherent Optical Receiver, which issued Oct. 20, 2009, teaches techniques for detecting symbols in the presence of a frequency mismatch between the received carrier (that is, the transmitter) and the LO laser. In the system of U.S. Pat. No. 7,606,498, SYNC bursts having a known symbol (or bit) sequence and periodicity are used to determine an initial phase error value Δφ0, which represents an average phase error of detected symbols of the SYNC burst and the known (or ideal) phase values of the corresponding symbols as determined by the applicable encoding scheme). Once the SYNC burst has been processed, the receiver switches to a data directed mode, during which the symbol phase error Δφ is updated after a small group of, for example four, data symbol estimates, and used for rotating the phase of the next successive group of data symbol estimates. The rotated data symbol estimates are assumed to lie in the correct decision region of the encoding scheme symbol phase space. Consequently, the most likely value of each transmitted symbols can be determined by analysing the phase of each rotated data symbol estimate.
The process described in U.S. Pat. No. 7,606,498 is unbounded, and thus can compensate unbounded symbol phase error Δφ. However, this also means that when the phase error Δφ becomes large enough (e.g. π/4 for QPSK, or π/2 for BPSK) a “cycle-slip” can occur, in which a symbol estimate can be erroneously interpreted as lying in a decision region that is adjacent to the correct decision region. This can result in the erroneous interpretation of every symbol (and thus all data) following the cycle-slip.
Techniques are known in the art for mitigating the impact of cycle slips. For example, U.S. Pat. No. 7,606,498 describes “forward and reverse” decoding in combination with Forward Error Correction (FEC) to mitigate the effects of cycle slips. The sample phase is effectively reset during processing of each SYNC burst, which limits the effects of a cycle slip to a single data block. Forward and reverse decoding further reduces the number of data symbols that are exposed to a cycle slip within any given data block. However, even with this arrangement, a cycle slip can produce a large number of errored symbols within a data block, so that a relatively strong FEC is needed.
As is known in the art, a given FEC method is capable of correcting up to a maximum number of errored symbols (or bits) which any given block of symbols. This known maximum number of errored symbols can be referred to as a “FEC budget”, which can be committed to correcting errors due to noise and cycle-slips. Naturally, the portion of the FEC budget assigned to cycle slips reduces the remaining FEC budget that is available for correcting errored symbols due to noise. As the symbol rate of optical communication systems increases, sensitivity to noise also increases, and so does the desirability of devoting a larger portion of the FEC budget to noise correction.
The ability of this FEC to correct independent symbol errors determines the relevant probability level to be used in determining a worst case or maximum symbol event, for example 10−3. Similarly, the ability of this FEC to correct cycle slips determines the relevant probability level to be used in determining a worst case or maximum transient event, for example 10−10.
Applicant's co-pending U.S. patent application Ser. No. 12/326,933, filed Dec. 3, 2008 teaches techniques for detecting and correcting cycle slips, which reduces the average number of errored bits (due to cycle slips) that need to be corrected by FEC. According to U.S. patent application Ser. No. 12/326,933, the optical signal is formatted with SYNC bursts having a predetermined periodicity, and a plurality of known symbols at predetermined locations between successive SYNC bursts. The format, content and periodicity of the SYNC bursts can be as described in U.S. Pat. No. 7,606,498 and Applicant's co-pending U.S. Patent Application Publication No. 2007/0092260. The format, content and repetition rate of the known symbols are preferably selected to achieve a desired balance between performance of cycle-slip detection and compensation on the one hand, and overhead on the other.
At a receiver, the detected signal is partitioned into data blocks, each of which encompasses at least data symbols and a set of check symbols corresponding to the known symbols within the optical signal. Each data block is processed to detect a cycle slip, for example following the methods described above in U.S. Patent Application Publication No. 2007/0092260. When a cycle slip is detected, the set of check symbols of the data block are examined to identify a first slipped check symbol, and a phase correction applied to data symbols of the data block lying between the identified first slipped check symbol and the end of the data block.
This process corrects errored data symbols (due to cycle slips) which follow the first slipped check symbol within the data block, and so these errored data symbols do not have to be corrected by other methods such as FEC. Any errored data symbols lying ahead of the first slipped check symbol will remain uncorrected, however, and therefore remain to be corrected by other methods. However, on average, the number of residual errored data symbols is one-half of the data symbols which lie between two successive check symbols, which will normally be very much less than the total number of data symbols between successive SYNC bursts.
The techniques of U.S. patent application Ser. No. 12/326,933 significantly reduce the FEC budget that must be allocated to correcting errored data symbols due to cycle slips. However, this benefit is obtained at a cost of increased overhead, and increased signal processing to detect cycle slips, locate the first slipped check symbol, and then correct data symbols following the first slipped check symbol in the data block.
Differential decoding schemes are also known in the art, and can limit the effect of a cycle slip to two consecutive symbols. However, differential decoding schemes suffer a disadvantage in that any detection error (due to any cause) will normally result in two errored symbols. In practical communications systems, this can result in a proliferation of errored symbols which exceeds the correction capacity of the FEC. Correct recovery of data by differential decoding requires that the corresponding differential encoding has previously been done to the data, which increases the complexity and cost of the transmitter.
Techniques for carrier recovery that overcome limitations of the prior art remain highly desirable.